Integral Equations and Integral Transforms
暫譯: 積分方程與積分變換

Banerjea, Sudeshna, Mandal, Birendra Nath

Integral Equations and Integral Transforms
  • 出版商: Springer
  • 出版日期: 2024-10-19
  • 售價: $2,370
  • 貴賓價: 9.5 折 $2,252
  • 語言: 英文
  • 頁數: 265
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 9819963621
  • ISBN-13: 9789819963621

    • 海外代購書籍(需單獨結帳)

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商品描述

This comprehensive textbook on linear integral equations and integral transforms is aimed at senior undergraduate and graduate students of mathematics and physics. The book covers a range of topics including Volterra and Fredholm integral equations, the second kind of integral equations with symmetric kernels, eigenvalues and eigen functions, the Hilbert-Schmidt theorem, and the solution of Abel integral equations by using an elementary method.

In addition, the book covers various integral transforms including Fourier, Laplace, Mellin, Hankel, and Z-transforms. One of the unique features of the book is a general method for the construction of various integral transforms and their inverses, which is based on the properties of delta function representation in terms of Green's function of a Sturm-Liouville type ordinary differential equation and its applications to physical problems.

The book is divided into two parts: integral equations and integral transforms.Each chapter is supplemented with numerous illustrative examples to aid in understanding. The clear and concise presentation of the topics covered makes this book an ideal resource for students, researchers, and professionals interested in the theory and application of linear integral equations and integral transforms.


商品描述(中文翻譯)

這本關於線性積分方程和積分變換的綜合教科書，旨在為數學和物理的高年級本科生及研究生提供學習資源。書中涵蓋了一系列主題，包括沃爾特拉（Volterra）和弗雷德霍姆（Fredholm）積分方程、具有對稱核的第二類積分方程、特徵值和特徵函數、希爾伯特-施密特定理，以及使用基本方法解決阿貝爾（Abel）積分方程。

此外，書中還介紹了各種積分變換，包括傅立葉（Fourier）、拉普拉斯（Laplace）、梅林（Mellin）、漢克爾（Hankel）和Z變換。這本書的一個獨特特點是提供了一種構建各種積分變換及其反變換的通用方法，該方法基於德爾塔函數在斯圖姆-柳維爾（Sturm-Liouville）型常微分方程的格林函數表示中的性質及其在物理問題中的應用。

本書分為兩部分：積分方程和積分變換。每一章都附有大量示例，以幫助理解。清晰簡潔的主題呈現使這本書成為對於有興趣於線性積分方程和積分變換理論及應用的學生、研究人員和專業人士的理想資源。

作者簡介

Sudeshna Banerjea is Professor at the Department of Mathematics, Jadavpur University, Kolkata. She obtained her M.Sc. degree and Ph.D. degree in Applied Mathematics from the University of Calcutta, respectively, in 1985 and 1992. She was NBHM Post-Doctoral Fellow at the Indian Statistical Institute, Kolkata, in 1993, before joining Jadavpur University as Lecturer in 1993. She is Fellow of the West Bengal Academy of Sciences since 2011. Her research interest includes integral equations, theory of water waves, and associated mathematical methods. With more than 68 research papers, she has supervised more than 8 Ph.D. students. Earlier, she was Principal Investigator for a number of major research projects sanctioned by NBHM, DST, and CSIR.

B. N. Mandal is former NASI Senior Scientist Platinum Jubilee Fellow at the Indian Statistical Institute (ISI), Kolkata (from 2009 to 2014), where he has been Honorary Professor (from 2006 to 2008), and Faculty (from 1989 to 2005). He also had taught at the University of Calcutta (from 1970 to 1989). He earned his M.Sc. degree and Ph.D. degree in Applied Mathematics, respectively, in 1966 and 1973, from the University of Calcutta. He was Postdoctoral Commonwealth Fellow at Manchester University, England, from 1973 to 1975. His research work comprises several areas of applied mathematics including water waves, integral transforms, integral equations, inventory problems, wavelets, etc. He has supervised 27 Ph.D. students and published more than 300 research papers. He was also Chief Editor of the OPSEARCH journal (Springer) and is on the editorial board of a number of reputed journals. He co-authored and co-edited a number of advanced level research monographs published by reputed publishers.


作者簡介(中文翻譯)

Sudeshna Banerjea 是加爾各答 Jadavpur 大學數學系的教授。她於 1985 年和 1992 年分別在加爾各答大學獲得應用數學的碩士學位和博士學位。她於 1993 年在印度統計學研究所（Indian Statistical Institute, Kolkata）擔任 NBHM 博士後研究員，隨後於同年加入 Jadavpur 大學擔任講師。自 2011 年以來，她是西孟加拉科學院的院士。她的研究興趣包括積分方程、水波理論及相關數學方法。她發表了超過 68 篇研究論文，並指導了超過 8 位博士生。她曾擔任多個由 NBHM、DST 和 CSIR 批准的重大研究項目的首席研究員。

B. N. Mandal 是印度統計學研究所（ISI）前 NASI 高級科學家白金禧年研究員（2009 至 2014 年），曾於 2006 至 2008 年擔任名譽教授，並於 1989 至 2005 年擔任教職。他也曾在加爾各答大學任教（1970 至 1989 年）。他於 1966 年和 1973 年分別在加爾各答大學獲得應用數學的碩士學位和博士學位。他於 1973 至 1975 年在英國曼徹斯特大學擔任英聯邦博士後研究員。他的研究工作涵蓋應用數學的多個領域，包括水波、積分變換、積分方程、庫存問題、小波等。他指導了 27 位博士生，並發表了超過 300 篇研究論文。他還曾擔任 OPSEARCH 期刊（Springer）的主編，並在多本知名期刊的編輯委員會中任職。他共同撰寫和編輯了多本由知名出版社出版的高級研究專著。

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